Incompressibility hypothesis

The value and the expression of this constant depend on the radiation type, as discussed below. It particularly differs whether one uses X-rays or neutrons. This range is therefore located at low -values, that is, at a resolution typically below q K. 2-3 nm". Under these conditions, the system can be considered a continuum This further leads one to assume that any point of the system contains a molecule or b [14]. This is the so-called incompressibility hypothesis [15], which leads to the following expression for S(q) ... 

The identity tensor by is zero for i J and unity for i =J. The coefficient X is a material property related to the bulk viscosity, K = X + 2 l/3. There is considerable uncertainty about the value of K. Traditionally, Stokes hypothesis, K = 0, has been invoked, but the vahdity of this hypothesis is doubtful (Slattery, ibid.). For incompressible flow, the value of bulk viscosity is immaterial as Eq. (6-23) reduces to... 

To study the viscoelastic case it is convenient to assume a constant Poisson ratio. This hypothesis is essentially correct in most cases. In fact, if the material is incompressible, one has v = 1/2. Taking the input as the applied force instead of the distribution p r), Eq. (16.177) suggests that the time dependence of the displacement for a viscoelastic materials is given by... 

This organization of the first LC layers, either spontaneous or controlled by the aligning layer, adhering to the solid, could lead to good lubrication since, in the vicinity of the surface, the movement is that of an incompressible LC layer over another LC layer. In 1981 we started some experiments to check this hypothesis. At that time, the idea seemed new and there were no known references. Before presenting the lubricating properties of... 

When Mam >0.3, the hypothesis of incompressibility no longer holds, and the gas acceleration leads to changes in the velocity... 

When Mam > 0.3 the hypothesis of incompressibility no longer holds and the gas acceleration leads to changes in the velocity profile not only in magnitude but also in shape. The magnitude increments produce additional pressure drop while the shape changes alter the friction factor at the walls. The continuous variation in shape of the velocity profile means that neither fully developed nor locally fully developed flows occur. This fact influences the convective heat transfer coefficient since no fully developed temperature profiles can occur if the flow is developing and the experimental Nusselt numbers differ by the theoretical values for fully developed flow. It is possible to demonstrate numerically that when the Mach number increases the Nusselt number decreases along the... 

Assume a thin ideally plastic layer connected with two rigid blocks. Cross sections of the layer at y = 0, y = /i stay planar. Since the layer is thin, it is reasonable to accept the hypothesis of planar cross sections, i.e. = M (y). The equation of incompressibility... 

Most soft elastomers are nearly incompressible and the adoption of the hypothesis of incompressibility in the constitutive equations allows for some simplifications in the analytical calculations. However, this choice has some shortcomings (i) die constraint/ = 1 poses difficulties in the convergence of computational algorithms when numerical solutions are sought and (ii) the stmcture of die constitutive electroelastic equations are not completely revealed because of die presence of the hydrostatic pressure. Therefore, aiming at elucidating the latter item, we prefer to formulate the constitutive equations and solve a relevant boundary-value problem, for a soft dielectric beginning from the compressible case. 

To overcome the limitations due to the hypothesis of volume incompressibility, Lacombe and Sanchez proposed to introduce vacant cells in the lattice model as a means to accommodate free volume (Vo). A system of m constituents would thus be mixed with o vacant cells and Vq/V would be the free volume fraction. Under these conditions the entropy of mixing can be shown to be... 

Hypothesis of isothermal incompressible steady laminar flow. The variation of the system physical quantities versus time can be ignored when arriving at a successive extrusion process. 

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